{"product_id":"biaxial-nematic-liquid-crystals-isbn-9780470871959","title":"Biaxial Nematic Liquid Crystals","description":"\u003cp\u003eIn the nematic liquid crystal phase, rod-shaped molecules move randomly but remain essentially parallel to one another. Biaxial nematics, which were first predicted in 1970 by Marvin Freiser, have their molecules differentially oriented along two axes. They have the potential to create displays with fast switching times and may have applications in thin-film displays and other liquid crystal technologies.\u003cbr\u003e \u003cbr\u003eThis book is the first to be concerned solely with biaxial nematic liquid crystals, both lyotropic and thermotropic, formed by low molar mass as well as polymeric systems. It opens with a general introduction to the biaxial nematic phase and covers:\u003cbr\u003e \u003cbr\u003e• Order parameters and distribution functions\u003cbr\u003e \u003cbr\u003e• Molecular field theory\u003cbr\u003e \u003cbr\u003e• Theories for hard biaxial particles\u003cbr\u003e \u003cbr\u003e• Computer simulation of biaxial nematics\u003cbr\u003e \u003cbr\u003e• Alignment of the phase\u003cbr\u003e \u003cbr\u003e• Display applications\u003cbr\u003e \u003cbr\u003e• Characterisation and identification\u003cbr\u003e \u003cbr\u003e• Lyotropic, thermotropic and colloidal systems together with material design\u003cbr\u003e \u003cbr\u003eWith a consistent, coherent and pedagogical approach, this book brings together theory, simulations and experimental studies; it includes contributions from some of the leading figures in the field. It is relevant to students and researchers as well as to industry professionals working in soft matter, liquid crystals, liquid crystal devices and their applications throughout materials science, chemistry, physics, mathematics and display engineering.\u003c\/p\u003e \u003cp\u003eAbout the Editors xiii\u003c\/p\u003e \u003cp\u003eList of Contributors xv\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eGeoffrey R. Luckhurst and Timothy J. Sluckin\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Historical Background 1\u003c\/p\u003e \u003cp\u003e1.2 Freiser Theory 3\u003c\/p\u003e \u003cp\u003e1.3 Nematic Order Parameters 4\u003c\/p\u003e \u003cp\u003e1.4 Nematic Tensor Order Parameters 5\u003c\/p\u003e \u003cp\u003e1.5 Theoretical Phase Diagrams 6\u003c\/p\u003e \u003cp\u003e1.6 Landau–de Gennes Theory 9\u003c\/p\u003e \u003cp\u003e1.7 Computer Simulation 10\u003c\/p\u003e \u003cp\u003e1.8 Other Theoretical Issues 11\u003c\/p\u003e \u003cp\u003e1.9 Applications 12\u003c\/p\u003e \u003cp\u003e1.10 Characterisation 12\u003c\/p\u003e \u003cp\u003e1.11 Lyotropic and Colloidal Systems 14\u003c\/p\u003e \u003cp\u003e1.12 Molecular Design 15\u003c\/p\u003e \u003cp\u003eReferences 19\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Biaxial Nematics: Order Parameters and Distribution Functions 25\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eGeoffrey R. Luckhurst\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 25\u003c\/p\u003e \u003cp\u003e2.2 The Cartesian Language 26\u003c\/p\u003e \u003cp\u003e2.2.1 Order Parameters 26\u003c\/p\u003e \u003cp\u003e2.2.2 Molecular Symmetry 28\u003c\/p\u003e \u003cp\u003e2.2.3 Measurement 30\u003c\/p\u003e \u003cp\u003e2.3 The Spherical Tensor Language 31\u003c\/p\u003e \u003cp\u003e2.3.1 The Order Parameters of Biaxial Molecules in a Uniaxial Phase 31\u003c\/p\u003e \u003cp\u003e2.3.2 Molecular Symmetry 33\u003c\/p\u003e \u003cp\u003e2.3.3 Measurement 33\u003c\/p\u003e \u003cp\u003e2.4 Extension to Biaxial Nematics 35\u003c\/p\u003e \u003cp\u003e2.4.1 Orientational Order Parameters 35\u003c\/p\u003e \u003cp\u003e2.4.2 Systems with D2h Point Group Symmetry 36\u003c\/p\u003e \u003cp\u003e2.4.3 Measurement of the Order Parameters 37\u003c\/p\u003e \u003cp\u003e2.4.4 Systems with C2h Point Group Symmetry and Their Order Parameters 38\u003c\/p\u003e \u003cp\u003e2.4.5 Systems with C2h Point Group Symmetry: The Cartesian Language 39\u003c\/p\u003e \u003cp\u003e2.5 Fourth-Rank Order Parameters 42\u003c\/p\u003e \u003cp\u003e2.6 The Singlet Orientational Distribution Function 44\u003c\/p\u003e \u003cp\u003e2.7 Appendices 47\u003c\/p\u003e \u003cp\u003e2.7.1 Point Group Symmetry and the Associated Symmetry Operations 47\u003c\/p\u003e \u003cp\u003e2.7.2 Legendre Polynomials, Modified Spherical Harmonics and Wigner Rotation Matrices 48\u003c\/p\u003e \u003cp\u003eAcknowledgements 51\u003c\/p\u003e \u003cp\u003eReferences 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Molecular Field Theory 55\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eEpifanio G. Virga\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 55\u003c\/p\u003e \u003cp\u003e3.2 General Mathematical Theory 57\u003c\/p\u003e \u003cp\u003e3.2.1 Two-Particle Hamiltonian 57\u003c\/p\u003e \u003cp\u003e3.2.2 Ensemble Potentials 62\u003c\/p\u003e \u003cp\u003e3.2.3 Molecular Field Approximation 65\u003c\/p\u003e \u003cp\u003e3.2.4 Variational Principles 69\u003c\/p\u003e \u003cp\u003e3.2.5 Local Stability Criterion 71\u003c\/p\u003e \u003cp\u003e3.3 Non-Polar Molecules 74\u003c\/p\u003e \u003cp\u003e3.3.1 Quadrupolar Hamiltonians 74\u003c\/p\u003e \u003cp\u003e3.3.2 Phase Transitions 80\u003c\/p\u003e \u003cp\u003e3.3.3 Universal Phase Diagram 87\u003c\/p\u003e \u003cp\u003e3.3.4 Steric Effects 91\u003c\/p\u003e \u003cp\u003e3.4 Polar Molecules 99\u003c\/p\u003e \u003cp\u003e3.4.1 Dipolar Fluids 100\u003c\/p\u003e \u003cp\u003e3.4.2 Dipolar Hamiltonian 102\u003c\/p\u003e \u003cp\u003e3.4.3 Condensed Polar Phases 107\u003c\/p\u003e \u003cp\u003eReferences 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Hard Particle Theories 117\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAndrew J. Masters\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 117\u003c\/p\u003e \u003cp\u003e4.2 Theoretical Approaches 119\u003c\/p\u003e \u003cp\u003e4.3 Board-Like Models 122\u003c\/p\u003e \u003cp\u003e4.4 Bent-Core Models 124\u003c\/p\u003e \u003cp\u003e4.5 Rod–Plate Mixtures 125\u003c\/p\u003e \u003cp\u003e4.6 Conclusions and Speculations 128\u003c\/p\u003e \u003cp\u003eAcknowledgements 129\u003c\/p\u003e \u003cp\u003eReferences 129\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Landau Theory of Nematic Phases 133\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eLech Longa\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 133\u003c\/p\u003e \u003cp\u003e5.2 Symmetry of Biaxial Nematics and Primary Order Parameters 134\u003c\/p\u003e \u003cp\u003e5.3 Landau Expansion 136\u003c\/p\u003e \u003cp\u003e5.3.1 Generic NU –I Phase Transition 136\u003c\/p\u003e \u003cp\u003e5.3.2 Generic NB –NU and NB –I Phase Transitions 138\u003c\/p\u003e \u003cp\u003e5.3.3 Role of Coupling between Nematic Order Parameters 141\u003c\/p\u003e \u003cp\u003e5.3.4 Landau–de Gennes Expansion in Terms of the Alignment Tensor 145\u003c\/p\u003e \u003cp\u003e5.4 Conclusion 149\u003c\/p\u003e \u003cp\u003eAcknowledgements 149\u003c\/p\u003e \u003cp\u003eReferences 149\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Computer Simulations of Biaxial Nematics 153\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eRoberto Berardi and Claudio Zannoni\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 153\u003c\/p\u003e \u003cp\u003e6.2 Order Parameters 156\u003c\/p\u003e \u003cp\u003e6.3 Model Potentials and Applications 159\u003c\/p\u003e \u003cp\u003e6.3.1 Lattice Models 159\u003c\/p\u003e \u003cp\u003e6.3.2 Atomistic Models 162\u003c\/p\u003e \u003cp\u003e6.3.3 Molecular Models 163\u003c\/p\u003e \u003cp\u003e6.4 Conclusion 171\u003c\/p\u003e \u003cp\u003eAcknowledgements 173\u003c\/p\u003e \u003cp\u003e6.5 Appendices 173\u003c\/p\u003e \u003cp\u003e6.5.1 Quaternions 173\u003c\/p\u003e \u003cp\u003e6.5.2 Angular Momentum Operator 174\u003c\/p\u003e \u003cp\u003e6.5.3 Kinematic and Dynamic Equations of Rotational Motion 175\u003c\/p\u003e \u003cp\u003e6.5.4 Propagator\/Integrator of Rotational Equations of Motion 176\u003c\/p\u003e \u003cp\u003e6.5.5 Gradient of the Biaxial Gay–Berne Potential 176\u003c\/p\u003e \u003cp\u003e6.5.6 Torques of the Biaxial Gay–Berne Potential 177\u003c\/p\u003e \u003cp\u003eReferences 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Continuum Theory of Biaxial Nematic Liquid Crystals 185\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eIain W. Stewart\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 185\u003c\/p\u003e \u003cp\u003e7.2 Continuum Model and Energies 186\u003c\/p\u003e \u003cp\u003e7.2.1 The Elastic Energy 187\u003c\/p\u003e \u003cp\u003e7.2.2 The Magnetic and Electric Energies 187\u003c\/p\u003e \u003cp\u003e7.2.3 The Total Energy 189\u003c\/p\u003e \u003cp\u003e7.3 Dynamic Equations 189\u003c\/p\u003e \u003cp\u003e7.3.1 Balance Laws 190\u003c\/p\u003e \u003cp\u003e7.3.2 The Viscous Stress 192\u003c\/p\u003e \u003cp\u003e7.3.3 The Dynamic Equations 194\u003c\/p\u003e \u003cp\u003e7.3.4 Euler Angle Description 195\u003c\/p\u003e \u003cp\u003e7.3.5 A Simple Shear Flow 196\u003c\/p\u003e \u003cp\u003e7.4 Equilibrium Equations 198\u003c\/p\u003e \u003cp\u003e7.4.1 The Equilibrium Equations 199\u003c\/p\u003e \u003cp\u003e7.4.2 Alignment Induced by a Magnetic Field 200\u003c\/p\u003e \u003cp\u003e7.5 Conclusion 202\u003c\/p\u003e \u003cp\u003eReferences 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 The Alignment of Biaxial Nematics 205\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eDemetri J. Photinos\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 205\u003c\/p\u003e \u003cp\u003e8.2 Alignment by an External Electric or Magnetic Field 206\u003c\/p\u003e \u003cp\u003e8.3 Surface Alignment 208\u003c\/p\u003e \u003cp\u003e8.3.1 Macroscopic Description 208\u003c\/p\u003e \u003cp\u003e8.3.2 Molecular Scale Description 210\u003c\/p\u003e \u003cp\u003e8.4 Flow Alignment 210\u003c\/p\u003e \u003cp\u003e8.5 Lower Symmetry Biaxial Nematics and Hierarchical Domain Structures 211\u003c\/p\u003e \u003cp\u003eAcknowledgements 212\u003c\/p\u003e \u003cp\u003eReferences 212\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Applications 215\u003c\/b\u003e\u003cbr\u003e\u003ci\u003ePaul D. Brimicombe\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 215\u003c\/p\u003e \u003cp\u003e9.1.1 Materials Considerations 215\u003c\/p\u003e \u003cp\u003e9.1.2 Surface Alignment 216\u003c\/p\u003e \u003cp\u003e9.2 Thin-Film Electro-Optic Devices 217\u003c\/p\u003e \u003cp\u003e9.2.1 Minor-Director In-Plane Switching Devices 218\u003c\/p\u003e \u003cp\u003e9.2.2 Electric Field-Induced Biaxiality Effects 220\u003c\/p\u003e \u003cp\u003e9.2.3 Planar Biaxial Nematic Devices 221\u003c\/p\u003e \u003cp\u003e9.2.4 Twist Effects in Biaxial Nematics and Biaxial Pi-Cells 222\u003c\/p\u003e \u003cp\u003e9.2.5 Bistable Biaxial Nematic Devices 223\u003c\/p\u003e \u003cp\u003e9.2.6 Spontaneous Chirality Effects 224\u003c\/p\u003e \u003cp\u003e9.3 Non-Device Applications of Biaxial Nematic Liquid Crystals 225\u003c\/p\u003e \u003cp\u003e9.3.1 Optical Compensation Films 225\u003c\/p\u003e \u003cp\u003e9.4 Conclusion 225\u003c\/p\u003e \u003cp\u003eReferences 226\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Characterisation 229\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Textures of Nematic Liquid Crystals 230\u003cbr\u003e\u003ci\u003eIngo Dierking\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1.1 Polarising Microscopy 230\u003c\/p\u003e \u003cp\u003e10.1.2 Simple Liquid Crystal Optics 230\u003c\/p\u003e \u003cp\u003e10.1.3 Optical Biaxiality 232\u003c\/p\u003e \u003cp\u003e10.1.4 Textures 234\u003c\/p\u003e \u003cp\u003eReferences 240\u003c\/p\u003e \u003cp\u003e10.2 Refractive Index Studies 242\u003cbr\u003e\u003ci\u003eAntonio J. Palangana\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.2.1 Introduction 242\u003c\/p\u003e \u003cp\u003e10.2.2 Optical Indicatrix 242\u003c\/p\u003e \u003cp\u003e10.2.3 Optical Conoscopy 244\u003c\/p\u003e \u003cp\u003e10.2.4 Results 246\u003c\/p\u003e \u003cp\u003e10.2.5 Acknowledgements 250\u003c\/p\u003e \u003cp\u003eReferences 250\u003c\/p\u003e \u003cp\u003e10.3 Orientational Order Parameters of Nematic Liquid Crystals Determined by Infrared and Raman Spectroscopy 251\u003cbr\u003e\u003ci\u003eJagdish K. Vij and Antoni Kocot\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e10.3.1 Introduction 252\u003c\/p\u003e \u003cp\u003e10.3.2 Polarised IR Spectroscopy 252\u003c\/p\u003e \u003cp\u003e10.3.3 Scalar Order Parameters of a Second-Rank Tensor 252\u003c\/p\u003e \u003cp\u003e10.3.4 IR Absorbance Components 254\u003c\/p\u003e \u003cp\u003e10.3.5 Experimental Method 256\u003c\/p\u003e \u003cp\u003e10.3.6 Results for the Order Parameters for the Tetrapodes 256\u003c\/p\u003e \u003cp\u003e10.3.7 Discussion of the Order Parameters 258\u003c\/p\u003e \u003cp\u003e10.3.8 Raman Spectroscopy 259\u003c\/p\u003e \u003cp\u003e10.3.9 Comparisons of IR and Raman Spectroscopy for Determining Order Parameters 263\u003c\/p\u003e \u003cp\u003eReferences 264\u003c\/p\u003e \u003cp\u003e10.4 NMR Spectroscopy 265\u003cbr\u003e\u003ci\u003eLouis A. Madsen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.4.1 Introduction: NMR Basics, Advantages and Limitations 265\u003c\/p\u003e \u003cp\u003e10.4.2 Probing Orientational Order 266\u003c\/p\u003e \u003cp\u003e10.4.3 Creating a Director Distribution to Observe Biaxiality 267\u003c\/p\u003e \u003cp\u003e10.4.4 Spectral Analysis Considerations: Fitting and Rotational Modulations 268\u003c\/p\u003e \u003cp\u003e10.4.5 Incorporating Deuterium: Direct Mesogen Labelling Versus Probe Solutes 270\u003c\/p\u003e \u003cp\u003e10.4.6 Powder Spectra and Monodomain Spectra: Examples 271\u003c\/p\u003e \u003cp\u003e10.4.7 Alternative and Emerging Methods 272\u003c\/p\u003e \u003cp\u003eReferences 274\u003c\/p\u003e \u003cp\u003e10.5 Structural Studies of Biaxial Nematics: X-Ray and Neutron Scattering 276\u003cbr\u003e\u003ci\u003ePatrick Davidson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.5.1 Introduction 276\u003c\/p\u003e \u003cp\u003e10.5.2 Theoretical Considerations 276\u003c\/p\u003e \u003cp\u003e10.5.3 Experimental Details 279\u003c\/p\u003e \u003cp\u003e10.5.4 Specificities of the Scattering by Different Kinds of Biaxial Nematics 280\u003c\/p\u003e \u003cp\u003eReferences 283\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Lyotropic Systems 285\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAntonio M. Figueiredo Neto and Yves Galerne\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 285\u003c\/p\u003e \u003cp\u003e11.2 Phase Diagrams 286\u003c\/p\u003e \u003cp\u003e11.3 The Potassium Laurate–Decanol–Water Mixture: A Working Example 287\u003c\/p\u003e \u003cp\u003e11.4 The Intrinsically Biaxial Micelles Model 294\u003c\/p\u003e \u003cp\u003e11.5 Theoretical Reconstruction of the Lyotropic Nematic Phase Diagram: a Landau-Like Approach 298\u003c\/p\u003e \u003cp\u003e11.6 Conclusions 302\u003c\/p\u003e \u003cp\u003eAcknowledgements 302\u003c\/p\u003e \u003cp\u003eReferences 302\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Colloidal Systems 305\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eGert Jan Vroege\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 305\u003c\/p\u003e \u003cp\u003e12.2 Onsager Theory and Extensions 306\u003c\/p\u003e \u003cp\u003e12.3 Special Features of Colloids and Colloidal Liquid Crystals 307\u003c\/p\u003e \u003cp\u003e12.4 Biaxiality in Mixtures of Rods and Plates 308\u003c\/p\u003e \u003cp\u003e12.5 Particles with Inherent Biaxial Shape 311\u003c\/p\u003e \u003cp\u003e12.6 Concluding remarks 315\u003c\/p\u003e \u003cp\u003eReferences 316\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Thermotropic Systems: Biaxial Nematic Polymers 319\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAnke Hoffmann, Felicitas Brömmel, and Heino Finkelmann\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 319\u003c\/p\u003e \u003cp\u003e13.2 Main-Chain Liquid Crystal Polymers 321\u003c\/p\u003e \u003cp\u003e13.3 Side-Chain Liquid Crystal Polymers 321\u003c\/p\u003e \u003cp\u003e13.4 Comparison of Attachment Geometries – Influence of Molecular Dynamics and Molecular Shape 327\u003c\/p\u003e \u003cp\u003e13.5 Conclusion 330\u003c\/p\u003e \u003cp\u003eReferences 330\u003cbr\u003e\u003cbr\u003e\u003cb\u003e14 Low Molar Mass Thermotropic Systems 333\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eMatthias Lehmann\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Preamble 333\u003c\/p\u003e \u003cp\u003e14.2 Introduction and General Considerations 333\u003c\/p\u003e \u003cp\u003e14.3 Single Component 336\u003c\/p\u003e \u003cp\u003e14.3.1 Biaxial Board-Shaped Mesogens 336\u003c\/p\u003e \u003cp\u003e14.3.2 V-Shaped Nematogens 338\u003c\/p\u003e \u003cp\u003e14.3.3 Multipodes 350\u003c\/p\u003e \u003cp\u003e14.4 Mixtures 354\u003c\/p\u003e \u003cp\u003e14.5 Concluding Remarks 360\u003c\/p\u003e \u003cp\u003eReferences 360\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Final Remarks 369\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eGeoffrey R. Luckhurst and Timothy J. Sluckin\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eReferences 373\u003c\/p\u003e \u003cp\u003eIndex 375\u003c\/p\u003e \u003cp\u003e\u003cb\u003eGEOFFREY R. LUCKHURST\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eSchool of Chemistry, University of Southampton, UK\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eTIMOTHY J. SLUCKIN\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eSchool of Mathematics, University of Southampton, UK\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eIn the nematic liquid crystal phase, rod-shaped molecules move randomly but remain essentially parallel to one another. Biaxial nematics, which were first predicted in 1970 by Marvin Freiser, have their molecules differentially oriented along two axes. They have the potential to create displays with fast switching times and may have applications in thin-film displays and other liquid crystal technologies.\u003c\/p\u003e \u003cp\u003eThis book is the first to be concerned solely with biaxial nematic liquid crystals, both lyotropic and thermotropic, formed by low molar mass as well as polymeric systems. It opens with a general introduction to the biaxial nematic phase and covers:\u003c\/p\u003e \u003cp\u003e• Order parameters and distribution functions\u003c\/p\u003e \u003cp\u003e• Molecular field theory\u003c\/p\u003e \u003cp\u003e• Theories for hard biaxial particles\u003c\/p\u003e \u003cp\u003e• Computer simulation of biaxial nematics\u003c\/p\u003e \u003cp\u003e• Alignment of the phase\u003c\/p\u003e \u003cp\u003e• Display applications\u003c\/p\u003e \u003cp\u003e• Characterisation and identification\u003c\/p\u003e \u003cp\u003e• Lyotropic, thermotropic and colloidal systems together with material design\u003c\/p\u003e \u003cp\u003eWith a consistent, coherent and pedagogical approach, this book brings together theory, simulations and experimental studies; it includes contributions from some of the leading figures in the field. It is relevant to students and researchers as well as to industry professionals working in soft matter, liquid crystals, liquid crystal devices and their applications throughout materials science, chemistry, physics, mathematics and display engineering.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988809367781,"sku":"NP9780470871959","price":224.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470871959.jpg?v=1761781676","url":"https:\/\/k12savings.com\/products\/biaxial-nematic-liquid-crystals-isbn-9780470871959","provider":"K12savings","version":"1.0","type":"link"}